A Wallis Product on Clovers
Trevor Hyde
TL;DR
This paper generalizes the Wallis product to a sequence related to arc lengths of clover curves, extending a classical mathematical result through integral-based proofs.
Contribution
It introduces a generalized Wallis product for new sequences connected to clover curve arc lengths, broadening the scope of classical analysis.
Findings
Established a generalized Wallis product formula
Connected the product to arc lengths of clover curves
Extended classical integral arguments to new sequences
Abstract
We prove a generalization of the Wallis product for a sequence of real numbers related to arc lengths of clover curves. Our proof generalizes a common argument given for the original Wallis product using a sequence of definite integrals.
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Taxonomy
TopicsChemical synthesis and alkaloids · Magnolia and Illicium research · Axial and Atropisomeric Chirality Synthesis